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SQUttlOHS POS TH£ ULCVIATIDH OF 
CHiKJIUTOGttFHIC FlSlilllUr OF MERIT 



JOE PRESTON FOIEl 



> OlSSERimON FRESeSTEO TO THE OKUIOATB ECHOOL 
OF THE UNIVERSin OF FLORIDA IH 
PARTIAL FULFIUNEHT OF THE REflOlREHENTS 
FOR THE DEQREE OF MCTOA OF FHILOSOFKT 



FLORIDA 



*COiakLei»H£l<TS 






(□OD-atandardlud) 



cunER 1 

UISO&liCUON 






Chi^iutagrBpny la a Hall-known oetnod for 
qHBntltatioQ of obaBlcal DoiaCiaa froiD a [saapla) nUlura. Over 
yeara aevaral oonoopta and pat*afflebBra » hareafbar- rafarrad bo 
a&roaabagrapUlo riguraa of nerlt (C?Ma) , Abvb Oesn Inbradosad 

tne CROHa are often difrinelt to aablaata Ctnoae whloh cbaractarl 

dataatlon (LOD)]. The goal of tba preeent work, Hlilcb la Introduoad 










t 



f f 

I m i f ! I f c 

J 

I > J‘£J $ J- i S e *- £■ ^ 










Qbromatogi'apblo peaJca 



Juatlflostlon of th 



of the oxponofltidlly ■odifled OauosUn (EHO), a 
tn* oonvolutlon of a Gauoaian fuoatlon anQ an 



deutoaetraca 



■31) tovolviiig tt 




peoantLy, BarOar and Carp dascPLOad a sanoal aetDod for CfOK 
auaotLta&ion wniob reaolraa Ule Brapnlcolly oeaauraDLe retantlao tLoa 

Intarbolaelona frov tciraa larse-acale universal eaiibratloo oupvas 
(31,12). 




t 



11 




1 1 
s 

I 



«iopI07eQ 80 Apple 11 Plue aieoooovputer. This neoeeelpePea , tnerefope, 
tbe dovelopaent of 8 aloplar aeciiod for eoeliutlna the £8)0 funotioo eod 
the InoorporatloD of a etopleri sore aoourate, anO nore senerel eat of 
alfiorlthee for obulolng the EHO dote of ioteraet. 



}f OeteotloB 



Le gaoerelly defined a: 



Tbe Holt of oeceoblon CLOD] 

laportaot flgore of merit In treoe enalyels, tbe LOD reoalne an 
amOlguoua quantity In tbe field of olu-oaatograpby. OeteotiOD Unite 
differing by orders of Dagnltude ere frequently reported for very 
Blmllar (aoaetlnee Identleell] obrosatogrepblo eyateoe. Suoh huge 
dlaorepenolee raise serious questions about the validity of tne LOD 
oonoept In ehroaatogrsphy. 

reetora the lotegrity of toa LOD oonoept, to aake tbe ohrosiatograpnlc 
LOD a reliable, aeanlogful figure of merit. Tble vUX be aocoapllahed 
in two steps: Plrat, the aejor souroea of the dlaerepanolas In 
chroastograpblo deteotlon Holts, l.e., the ourrent problems with tne 
LOD oohoept, will be identified. Saoond, eaoh problem will be addressed 






flWCTIOS 



OenEKATlOH 



eTftluAtto^ tbe fitto fiinacion 



tne laprovMDinta fignleved by this study is 
SDd is obtalaing the EKG Oats of isterast. 








Equation 



tns retention 








eoDvenlent to group tOe renge of poealble s veluee Into three reglone: 
eJ 0 i -3: b)-3 i a < b; and oj z 2 t . In region o» the definite 



InCegrai OQuala tna oonataat (v)'^ to wltbin D.01) aafl la tnua 
virtually Independant of a. In reglono a and P, houever, tba ralatlva 
value of tna definlta Intagi-al la hlably dapandant on a. Hunaroua 
teohnlduee poraU the acounate evaluation of I, In region 0. In region 
a, however, ae t haooaee oore negative. It oeooaea Bore dlffloiUt to 

la pertinent to aKaalne the practical olnlaum valued of a for EHG paaka, 
la seen froa aq 2,2, a dependa on a) the noroallaed dlfferenoe 
between the tlM of Intareat, t, and Oq! and b) the reolprocal of the 
peak aayaaatry, (T/og)~^. For a given peak ahape Icooatant v/dn), a 
Mill therefore be staalleet Caoat negative) at tba atartlng threahold of 

leading edge of the EHO peak where the value of the funotlon [hQ^ltl] 
la a apeolfled fraction, B, of Ite iDaalaus value, i.e., b,^n(t)/hp s B. 
Moreover, the aiolauo b value will deoreaae aa tba atartlng threahold la 
deoreaooO. Ibis la ahown In Table 2. 1 where olnloua a valued are 
tabulated for BMC peake with aBynoetrlee ranging from 0.1 to 3. Anotbor 
trend llluatrated le that for a given atartlng thraahold, Inoreaaea 



(In eq 2.1) evaluated? Bkoept for a vague referanoe to an unepeoifled 
polynonlal approxloatlon <30), all prevloua oetnoda for oaloulatlng I| 
aeploy different teohnlguaa for different valuea of a. for ■oOerate b 
valiiea le.g., reglone b and o, above), aooe oetnoda utllliad the well- 



preventing 




The Integral in eq 2. it ean he approzloated by a polynoeUL approzlutlan 
la(»<0) • «f(i) Pig) and IglsiO) a I- lalaeOJ. where 
ttPla) e S!tpC-e^/aJ/l2e)^^^, Pig) a tjjq * bgfl^ ♦ bgQ^ * bgg^ a b^g®, 









?gl7Ti0Bi&l ApproziBBtion 



0.3193S1530 

-0.3S63637<!2 



63 = 1.781W93T 

6, = -1.621255976 

bj = 1.33027S1129 






i! 

. . . 

Mias-'''’ 



Utu 



3- ? i 5 i 1 1 1 n 



•5 

n 



UU^ JS 
^ i ! ! ; : ! i I I 

i - ? ? ■ : 



5 






requiring Junt a fev prograasalng llnea (see llnea 2S9Q-31&0 In Appendix 






runolioa routine 

















o&lQulatfl t&e UQlvQraal data: and tg (aae Figure i.O. Hote 







isiL-ii iilci 






! SI 



n 

I 



n i n 
Sim 
! 1 1 n 
i M n 
n I n 
nil! 

! n n 

i i i 11 

! ! I ! I 

n M i 

S S ° S 5 



!i 

I f 

3 3 



! ! 
JJ 



Thou^ tbs exponentially aodlflsd &sussUn [BHC> 
Its uaa^s nlfht Qave been stUl aors sxtsnslTs nad 11 
evalnatioo reported previously. Hopefully 






BQUmONS 

FKXJUeS 



IP CHROHiTOCIUPHIC 




«li«ioated; and flnallp, two GPOMa propoBad onlginall/ in tiila work 
which deioonatpate how peaJc aayBiBctpy Orastioaily reduces ahrcaacofTsphic 
eftiolBiioy— the pelatiwa ayates amoleooj, Hhi, and the pelatlve pUto 


















Dertyad 



-- 



' C("aax - “»y5’'"»a*' ‘V's^ 

■ to ♦ " 

" "S® • 



= 31;* - eco* T* » 9 y* 

« . 3 



r«arranged to glvo 







Sino» tj, B/*, and , are graphloally oeaauraala, all the 
raaalBijig CBOHa can be calculated cnee the rundaaantal paraiaetera Oq, t, 







IHe CPOr) eQUBtlona v«r« dtfvelaped by ujiHelghted least squares curve 
fitting. Ttie relatloasblp betaeen several quantities te.fi.i REtdl, 



Becanse slDllar relationshlpa 
above, least squares fitting i 



I tavtflles 



initially Judged Oy 
CPM equations. 



'O aossrved In 

United to aOoul the sene ty^ renge 
fittings of the various 8/A textfilee were 
e aeeuracy and alapliolty of tne reaultlog 













2 . . 



I 



. n ? n i n 

i ? : ? ? f ? ? ? 

5 5: 5 5 5 5 5 ! 

H 5 ? 5 ! 5 5 ! 




'i 'i s I 3 i 

> > I f J f 



I 5 
I I 

I I 

li; 

I Is I 

;5E?5I 

' I 



SIP! 

3 llii= 

ilHii 

ftiyn 

liJIJlJ 



*" r s" r" f /!• ^ k“ 

2 =• = I I « f I I 



Except fer eqs 11b, 13b, and Ibb whloh bad bladdd of *0,976E, 

and *1.111J, raapeotlTsly, tbe Dias for every equation liven In 



relative atanderd (UDJ 



liolta obtained via propagation of error theory 









Gaueelan equatlone, i 
(311 la oonpared for 1 

ESDCHq^^) V The ellgOtly 

;he EKG equatlooa la due to unoertalnty 
'ed for the Gauaalao aqaetlona. The 
eooewhat larger IPSOa for the oethod of Barber end Carr are probably due 






The preolalon of the reoalnlng CfOMo In Table 3.2 vaa found 
blghly dependent on the peak ehape. Bather than reporting BSD 11 
the BBPe for eeveral CfOHa or groupo of CfOHa have been plotted va 



Listed Id Tables 3.3 and 3.1 are smaller sots of CfOK equations 
developed only for use In deterslnlng If a real ohroDatographle peak Is 

oaloulate any CPW llnoludlng since they are usually less 




i: s I I I. 5 

^ ; ; JliJjfiji 



Ai i i I 
ii ? 2 s 



5 s 

i ? ! 




I i 3 

• I I 

! ■ I 

! ? i 

Mm 



:! 






IH! 

lifii 

Hi's 

(fiji 

a- i I j:- h 
; ; ; II iJJiJi 



I 

= 

j 



SselMtlng «,y,, Nj, and 



OBUdratlod oi 



rteportdd an paroant ralatlva atandard daviatlon 
Praoladon or aquatlana eatloatad via aproi' propasatloa, 




asb% 



aodftllAg deolslone 



LI sofficlent tc 






arror propaEBtlon analysia foi 
tala aaalyaia. Tna RSDa of 



for iadlviilual peah 



abapeo lat a sLron peak height fraotloo) ware averaged i 
previoualyt therahy ihpltcitly aaauolng toe Independehoe of the 



originally reported relative to Og, oq, and CB/A - I) , reapeotlvely, 
HhlUplloatlon Py eg/t,,, i'q/II,. and (B/A - oonverted thea to 
the appropriate fora. 







1. ChroBAtograjs recgrdlng rate: 1 (Hg , ^4.3 cal 

2. Ruler reaoLutloni ± 0.2 ibb 

3. Hlnlaiua reteneloa dUtanee. 10 ca 

4. Hlnlaua paalc height, 10 am 



flesulea*’® 



idantloal 



CB/A)^ i2.0 ^2.5 ^3.5 

Oata oDtalTied fpoo rareraace 50 ana auheequtntly aonverted (aae 
iaterpalatad far a s 0.3. ' ^ resuita 



Asaumlog nagliglCie 



. IKBSIXt,))* . 4[ilSDtH,)]® • 
SSDC!B/*1,1^ * 



14 wltQ (B/A)^ Because of Cara 4, Clearly tbie Tariatlon will be 
It far -(S^Alj < Cg < 0. AflbltlMally, as Cg *-tfl/A)^. 
ig) * *• Bor Cg s 0, RSDCBgyg) la aasentlally Inbepeodafit of 
Finally, for Cg > 0, a negligible to alight yarlation oB 

I than 0.51 for 1.00 i B/A i B.T6. 

le reaainiag CFCMa (t, t/^, BFL, H,, Ht.,To,Tg) oonpriae a aeoond 



Figure 3.1 shows. In every loatanoo the iaprecialon is largest for the 
Anslyaia of the error propagation equations ahov that one or more taraa 




at 101 peak height rather than at other peak height fraotions suob as 



i=-“3>S 











s, sr 

!i. 






§ I 
1 “ 
II 





dOddS lN3Dd3d 






aquatloo 
BS6 = 1.04 



ase .. 

RSE . 0.913[(B/*)o,55]"*'25 



Ta^en 0OU«atl7el7, the ahove erguoente Inhleete that the best C70H 
eetlaation le obtained fnao graphical ohroutographlo aaaaurenenta at 
101 paajc beisht. 



'iaual Inapaotion anC 
la uDUKalr event Chat 



a Gauaatan, £HG» or other i 
aen froa the aayvaeCry fac 
3/i - 1 , the validity of 






Par slightly aayaeetFlo ohrooatographic peaha, the aasignnent of 
B/A (e.g., la a paaa with B/A a 1.03 a 0.02 Oauaalac?). InsoPar as 






1.00 t B/A < 1.09. Plgiir# 3.3 












%6 

1 -“ 

jlj 



S|1 





HoaaB iN3oa3d 






Impraolalon, tbou^li far B/A > 1.04 tna EnG 
Piircneraora, aa aaen froa Table 3.5, tfle eban^a In tha oraoUlon of CFDH 
aatlnatlon raaulting froa panic ODdal alaaaatsnaarLt aould be laaa 








arbitrary data trimeatina. Thla waa probably tha aouroa of btaa la our 
statlatlcal moeant aatbod aa well, but ragardlaaa of tha aouroa of biaa 
tna aaaa oonoluaion oay ba drawn: at high aaymaatrlaa (2.05 < 0/A < 



Warlclaa panaa of ena eauaticwia . Tha BMQ-baaed agoationa tn 






ecrioiBnoy, t 



particularly uaaful. Per «Katnplc, th« Cect pcsalble 
OBC Ce relBteC vary aiaply to the true ohroaatograpMo 



^ (oalouUted vJ 



, tpls apprazlMtlan la good Cc 



BodereCo to nigh ofrielanoy ohrooatagrapUlo eyateaa. 

Altnough B/A, ASS. and RFL era tsutually irtardopandeot (i.a., onoa 
B/A baa baeo aaeaured R3E and RPL aay ba oaloulated], tba apeolPlcatlon 



aorroapoadtiig RSg a isi or RPL ■ proaidoa a olearar Indloatlsn of 
tba actual afrielaooy and bov auob rooQ for ImproTcaant exlsta. 

Figure 3. a abows tba axponantlal-llka relatiooablp of BB£ and RPL 
altn B/A. Cbroaatograpblo ayateaa wltb aayBoatrlaa of i.QO and I.IO are 
oparatlng at nuoh dlffarent ralativa offloianclaa, wblle two ayateoa 
oparatibg at B/A a 2.00 and 2.10 ara raallalng nearly tba aaoa relative 

lot aa auQoaaaful aa tbet already deacrlbed. In tba 






100 







polynODlBXs. 



approach yleloeil equationa 










ooaalaeriiOly aora 




CUSmCAtlOK 



CHAPISA 4 

OF THS mil Of BJTECIION IB CBSOMAIDORAPai 






In chli ohipter, the foeua is on ellolnettnB the oonfuatcin 
euproundlng the limit of deteotlor (LODI In ohrometography. Some prior 
knoBledge or the LOO conoept La aaauoied. Thla dlaooeelon primarily 
appLlea to Doth gaa and liquid ohromatography using oonceatraclon or 
aaaa senaltlee dateotors uhoae output is measured as peak height, though 



apply to analyses using peak area as wall. Ideal linear elution, l.e,, 
Oausslan peak profiles, Is aasumed though moderate deviatiooa oan be 



Identifvin. Curran. Prohlene 



Initially, to determine the sources of dleorepanoy In 
ohromatographlo detection limits, me conducted a limited survey of 
analytloal textbooks, cbromatographlo monographs, and the primary 
ohroaetograpnlc literature. This survey revealed tmo miatakee ef 
omlealon, ae well as four major aouroea of dlaorepanclea. All six are 



juomarlsed Is lahla k.l. The first two problems are OUtsnt omlsslone 
wbloh dlacredlt the work reported, at least to some degree. However, 
they oan ba aUmlnated If eora attention le given during maauoorlpt 



may be dlsmtssed without further diseusalon. 






Th» llAit of oecoatlon has unfartimateLy Desn CDOfuoad with torao 
otbar oonoepta — particularly tbe Colntauis] dataetaDUlty— which arc siao 
uaaC Ih oDaractarlElng ohroaatograpnlc trace aiialyaes. Tatla 4,3 
includes ayobola and daflcltloBC for all four of tbesa coneepta. 

Table 4.3, partioularly the HD, la tbe redundancy In noncnclature of the 
deteetloo licit and tbe HD, as eeidenced by tbe partial, but 
repraaentatlve list of Capparent) aynonyce for tbaae ooneepta <ahovn in 

rafluBdant terBlnclosy lb soienea only aeryea to confuse. Thin Is 
especially true aben tbe apparent synonyHs for different ccccapta are 
I alollar. The use of these apparent synonyna should fie 

Even It the oonfosloo resultins from the redundant temlnology 
could be ellDlbated, the LCD eight stUl be confused with the HD by the 
apprentice ohronatograpber baoauae tbolr definitions, as ahoun In 

neaning, howseer). 

LOO B arbitrary cetactor signal leral/S {4.0 

let despite thalr oinllarltlee, tha LOO and MO are dlstlnot 
oonoepta, aa a oloaer aorutloy of Table 4.3 shows. Tbe LOO Is a general 
concept obaracteruing any oweraU trace analytical prooedure consisting 
a specific tern ohsraoterlelng 



dlaooctlnued Ic 







LOB . [Kj,U.Ic>/I|'^* 3 b HD (».3) 










aroltrary el£na>L-t 
arbitrary S/H lavel! 



laed, ranging froa 2 to 10. To Turtner ooaylloata 



apaoirlaii in aany Inacancea. 

Tdcss inconaiatenoiea and anfitguitlea are not aurprlsing ainoe (to 
our knowledge] no atandard oodel ror the USD has ever naen proponed, 
nuoh lens adopted, Dy any reeognlaed organisation for the field of 
obronetographyl Va oota apecifloeily the OBlsnien of an LOO definition 
in ohroaatography Oy the Aaerican Society for Teetlng and Materials 

other organiaationa ia alao euoatantieted in two reviews (na,43). 

More iaportantly, however, the shove loooneiateneiea and 
anbigultiea onn he eliminated ooepleteiy if a olaarly stated LOP eodei 
la adopted. Therefore the adoption of, with oinor reinterpretation, the 
lUfAC Bodel for apeotroohealoai enalysia (44) or a sodel Oaaed on first 
order error propagation (10] is proposed. These Bodala are given in 



SnvironiBsntal Cheoistry reaffirned tni: 










I ftoployed, 



laAd, Is computstlanslly eisplsr srtd nss slrssdy I 
1 Infrequsntly, tn Che ahraaaccrgysphic llteraCurs. On the other 
the error propasatlon model la not really all that eoapllosted; 
lookat oalculators with linear regression oapablllty oen Oe easily 
T toe error propagation Bodel. Furlbennora, the error 
propagation LOO model takas onoertalntles of tho slope and Inleroopt of 
tna oailbrallon curve Into aooount, resulting In a more reallatlo 
nuaerloBl estimate. 



developed originally 






analysis. Nearly 



t ctiTMaSogNphia buellne i 



matrljc), etc.] have identical, atralghtforvaj^ Interpretations i 
Intuitively it ia clear tbat tt 
to Sg aa tna staiidard devlatlco of tCe chrcoatographio baseline (noise). 

analyte's retaotien tine in the absence of the analyte (uben a tlanlc 

tbs blank signal (at the analytical vaveleogtn) in speotroseopy. Such a 
lllaral procedure would reculrs at least 20 injeollone of blank solution 
(SO blank ohrosatogransl) and is obviously too iapraccioal: 



'he retention 1 



Ik ablution, 
of the analyte would need to be known t 



e prsotlcal prooedure bf 






i (periodiol 



“signal ' range/p (l|.6a) 

for the oeasureigent of sg, it should be noted that the range is 
aculvalant to the peak-to.psak noise of the baeelino, H , if the 
letter ia Dsasured over a auffloieotly wide region of the onronatograo 
wnlob iooludea tbe analyte peak. Additionally, the baseline usually 






1l.J = <=lnj ’l«J 



(U.9) 



aq 4.9 It is clsar Chat tbs oonoeDtration of analyte Injeotad, 
La Oiractly proporcional to the aisouiit of analyte injected. 

^InJ ' ’inJ^'lDj 

irsfors tbe relatiye LOD (in unlta of oonoebtrstlonl, C, , is 



=L ■ iL^’inJ 

Though reaehed in a etraightforuard oanneri 

I is neverthelsaa false. Tbe error in ressobing is beet deeeribed 
I iaproper or inooaplete analogy. in going from a true etpreeeion, 
Ifl, to a false atateaent, eq 4,11, and were replaced by 

Liaiting quantities end q^, respeotively. Ho analogous 

aay vary oontlnuousiy over D < V,„j < .hers le 

4 nunerloal example irij.1 help deaonstrate the abaurdlty of eq 4.11. 
Suppose the trua, absolute LOD (qj^J for analyte X bad been deteralned 
independaotly by two aelentists using the same LC syebeo to be 1 x 10*'^ 
mol. If the soiaotiats had used different injection volumes of 5 uL and 
30 uL, aooording to eq 4.11 the relative lODs (C|_'sl for the eaae 
onrometograpnlo system would bo 2 a lO'^K snd 2 x 10 ‘‘'h, rospeotlvoly. 
Clearly eq 4.11 in ioapproprlete. 

4.12 below, la obtained by using 



IS difficulty in obtalolng a eonslstent, precise ee 



V'lnj,. 



problta 







iloglg progicrUiiniUCy osaatast, i. lUerutUaly, alnoe : V^(1 • k1 
aad » = CV,/=,)2, ag,.y writ. 



Kbare Vjj Is the retention voIUM loorreated fop oonpreultiuty in flC) 
end 0y is the bandwidth of tha dhroastograpbio paak, in eolnne unite. 

Equations d.15-V.IT are equivalent, end any one or then nay be used 



to derive an ejcpresalon whlot aooounta for tne affeota of these 
ahrooacOEratWilc paranatara on the tOD. Far slnpllelty. we use eq 4.i7. 















■- t«,/Kjj'/2 q,,, 

Its * i(«2 * 1)/(k, . 1)1 CBj/llj]''* U(_, 



of the traoe ouli'eiB. U etoaW Oe notea, I»»e»er, that the deteotloo 
LiBlta oannat ne lowered Infinitely by suon ieprovenenta. Eventually 
the anelyale will he optleizea to the point wBere further Isprovemente 

helpful. 

Conslaer two suoh doteotlon llnlta obtained uolng different 
that the latter would require an additional 



hhlohever way la ohoaen, it ehould be reoosninad that tt 






Inferred. 



subsorlpte "ref and "exp" refer to reference and 
reapectivaly, Slallar enuatlona raeultlng fron the 




IstataaJ. Given 






tbe analyat now haa a nathod for eoaparlng 
acre LODs aeaswrod under different 

experimental LOUe (aeeeured under different experlaental etates) were to 

On tbe other hand, the referanoe atatea by deflnltloo auat be 
vary oooaldarably In Liquid chroaatography CLCJ, paowed oolumn aaa 










rlt fop the oToraLl onrofflatogpaphtc aiulysls, but aa a ftgura of maplt 
p tha deteotop aa wall. The need fop the BiniiDua deteetabUlty CKD) 
a aeparata peraBatar fend hanee, tha oead fop a deteotop oallbratlon 
pva) would therefore be eliolnatod, reaultlag li 







ref«r«noe vilues for tne lodlvldiul parametera uara atleotad In 
>r CDOre of efin following oritarlai 
^ '**hi***a''* ^ loteraodlate ohromatograpMo perforaanca 

Baoufaotcrar npaoif toattona. **'* 



». 67). 



uoa repoptad dlreetly in tha 

Qln a pravloualy recoonnded rartga [k only— aae 
vaiuea aalnctod for tna ohroiaatograplilo nandvldtn ooaponsnt 
po siren la labia 11,4, TBe ranultlng raferanoe atabes and 
oorraapondlns alaodardlzad LOD aouatlona ara ahoHo In Tania 4 5 

Table 4.6 and tbe adrentasea aaoaaratad aarllar oonyanlantly 
aunaarlaa bba Bulk of toe material praaaotad in tnia aaotloo, Only one 
aOdlUonal point naada to be xadai oon-atandard (aaperioantal) 
bandMldtbj are beat oaaaurad dlraotly ualng aijuatlooa auoh aa 

"o ' V*' (4.29) 






IP different iaterpratationa are i 






taDle 4.1). Propos«d v&luea for the eoaponent paremetara 
of tha ohroaiBtogrephio refaraooe eteCea 



oerr^apoadUtg chrMatograpnle rafereace'atataa 







SUCOESIIOHS FOB fUIURE VOtK 




And finally, the relative error £R£J approaeh jaed so aueoenfully 
la the derlvatlQB of the e^uatloae in Chapter 3 le coopletaly general 
end ehoiila he ooaeldereo oy other aelentleta for any eenl-eeplrloal 



nodal lag 



USTIHQ OP TH£ 



BMC-U. the BASIC program hhlch evaluataa the EHC function and 
obtalna the imlreraal data, ta Uated below. In aoiUlon to the 
doomeotatlon supplied ultoln the program Ueelf and the flcwohartj 
given la Pig B.I, the folloulng should he noted: 

1. By letting S . oj/j and Y » a-e,.}/05, eq 2,4 can bn wUton aa 
haglt) = lAS«e)''2] „p,s2^ 



2, To the extent ellound by BASIC, the ayDbollan uaed In EHC-C 
oonaiatent ulth that In eqs A.l and A. 2 and elaeuhere in the tax 
firanli aymhola uere spelled out partially or entirely. 

3. £«u-lj uae developed on an Apple II Plus computer end optlmlied f 

0,1 i T/a^ s 4 using tg = 100, ■ 5, 0.001 i dtgjg i t, and O.ODI i 

< 1. hlnor modlfloatlona may be required for optimum performanca 



0 evaluation subroutine (lines 1 






fiiiiiiii is isii s isii i i' si ? 











ROUIIKS 




3S35S ssssSdSss; 




/ S3535 5SSS5;;553 



'■o.3''’s 




iPFEUOIX C— DMIVATIOH 






















s, gr™x-‘ ■■ "■ 

£:“gf ;a:s:',;,gr' “ 







si..;r;£ji„r"i™ri^’Evrs^^ 
!i'„.5:.“;::: s;i;; £r. “:r;;s-:;s ss!““ '■ 







s:..,“;;rgSH,sr “ ■™“‘- 

s,.n:s^i!;. ;;‘rs.s“:‘- sr;. “-ris 



;;!;,s‘;!‘s.s;,s =: s:=; sf.s;rs,s'' 




MOGKIFHICSL SmCH 



Joe Frestoa Foley ues horn In Lenlngeoo, Eentucky on Qolober 23, 
I93h. He grew up on a llveatooK and tobaooo Fara outaide Versailles, 
Seneuolci', end aeioodod the Hoodford County publlo schools. Hla early 
adolescent Interests Included oaoplng, sandlot football and basketball, 



eofflic books, flreuorks, model i 
fallen asleep uhlle sunbatblog) 

Assembly. As he entered Voe< 



je aaploratlon. 



)ol, Joe UBS eleoted President of 
^be statewide Junior Kentucky louth 

I and varsity tennU. In June of 
. be graduated with bigbest dlatlnotlon (oo-Valsdlncorlsn) , 

Irurlng the nest four years Joe attended Centre College of Kentucky, 

I be was induotnd Into Phi Beta Kappa. He reoslved ohemlstry awards 



Bacbelor of Soienoe In obeaistry ar 






Policy Studies. 



Collsge, bU oiaB uc«r, for e 



appoliitseat as a physical 



tJoa Oegaa bis graCuats acuby in onsBlstry at tbs Unlaaraity of 
Plorlda m June of 1979. In May of 19S3 be uas ona of slsaao grabnaca 
atudants aalaoteb nationally for an Aoorioan CDealoal Society Division 
of Analytical Cbanistry fallowabip. Later in 1983 be oospleted the 
roQulranante for tba dagrae of liootor of fbilosophy In analytical 
efleoistry end acoaptsd a National Aaaearob Counoil Poetdootoral Aasaarob 
Aaeoeiateanlp at the National Bureau of Standaros in OaithersOurg,